Related papers: A practical heuristic for finding graph minors
We present a dynamic programming algorithm for optimally solving the Cograph Editing problem on an $n$-vertex graph that runs in $O(3^n n)$ time and uses $O(2^n)$ space. In this problem, we are given a graph $G = (V, E)$ and the task is to…
In this paper we propose a new problem of finding the maximal bi-connected partitioning of a graph with a size constraint (MBCPG-SC). With the goal of finding approximate solutions for the MBCPG-SC, a heuristic method is developed based on…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
In this paper, we prove that for every connected graph G, there exists a split graph H with the same independence number and the same order. Then we propose a first algorithm for finding this graph, given the degree sequence of the input…
Given any graph $H$, a graph $G$ is said to be $q$-Ramsey for $H$ if every coloring of the edges of $G$ with $q$ colors yields a monochromatic subgraph isomorphic to $H$. Further, such a graph $G$ is said to be minimal $q$-Ramsey for $H$ if…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is…
The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…
A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper we solve the minimum linear arrangement problem for bijective connection graphs (for short BC graphs) which include hypercubes,…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
The Euler tour technique is a classical tool for designing parallel graph algorithms, originally proposed for the PRAM model. We ask whether it can be adapted to run efficiently on GPU. We focus on two established applications of the…
A graph G is called "minimalizable" if a diagram with minimal crossing number can be obtained from an arbitrary diagram of G by crossing changes. If, furthermore, the minimal diagram is unique up to crossing changes then G is called…
Chirality is one of the important assymmetrical property in wide area of natural science, which has been studied to predict molecular behavior. One of good methods to analyze molecules with complex structures is representing them as graphs…
The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal…
The graph partitioning problem has many applications in scientific computing such as computer aided design, data mining, image compression and other applications with sparse-matrix vector multiplications as a kernel operation. In many cases…
Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly…
The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…
A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics…
Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the…
Statistical analysis of large and sparse graphs is a challenging problem in data science due to the high dimensionality and nonlinearity of the problem. This paper presents a fast and scalable algorithm for partitioning such graphs into…